arXiv subjects

Jérôme Ballot

Publications and source records attributed to Jérôme Ballot.

At least 19 recordsLinked to original sources

arXiv2026

Bolometric corrections of stellar oscillation mode amplitudes as observed by the PLATO mission. I. Planck-spectrum estimates

We derive bolometric correction functions for oscillation mode amplitudes observed by the different cameras of the ESA PLATO mission. Such corrections between bolometric (full light) and mission instrument-specific amplitudes enable comparisons to theoretical expectations and amplitude conversion between different photometric missions, which is essential for proper detectability yields and target selection. Bolometric correction functions were calculated assuming a Planck function approximation for the stellar spectral flux distribution. The calculations follow the procedures applied in earlier analyses for the NASA Kepler and TESS missions. We derived power-law and polynomial parametrisations of the bolometric corrections with $T_{\rm eff}$. We find that on average, oscillation mode amplitudes from PLATO's normal cameras (N-CAMs) are expected to be ~6.7% lower compared to Kepler, and ~12.5% higher compared to TESS. A significant average amplitude ratio of ~25% is expected for amplitudes measured using the blue PLATO fast camera (F-CAM) compared to TESS. We find that observations of bright solar-like oscillators, especially with PLATO's F-CAMs, would provide an important test of the predicted corrections.

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arXiv2026

Seismic detection of core magnetic fields in red giants using the gravity offset

Magnetic fields are known to efficiently redistribute angular momentum in stars. They have been recently measured in the cores of red giant stars using asteroseismology. It was shown that core magnetic fields, if unaccounted for, can bias the measurements of the gravity offset $ε_g$, which is otherwise well characterised for red giants. Exploiting this bias as a way to detect magnetic fields in the cores of red giants, we wish to increase the number of magnetic field detections in red giants, but also to establish a method that could be widely applicable to all red giants. We selected 218 Kepler red giants showing abnormal measured values of $ε_g$. We used robust statistical criteria based on the expected lifetime of mixed modes to identify significant modes. We then adjusted an asymptotic expression for mixed modes to the observed frequencies, taking magnetic field and rotation into account, using Bayesian inference. We then assessed the probability of magnetic field detection and measured the magnetic field intensity using stellar models for the favourable cases. We found new magnetic red giant stars with fields ranging from 34 to 260 kG. For these stars, we measured values for $ε_g$ now in agreement with the expected value. Adding these new detections to those of previous studies, we showed that the mass distribution of magnetic giants is similar to that of the complete catalogue of red giants, but different from the mass distribution of red giants with suppressed dipole modes. We also found that the core rotation of magnetic red giants follows a similar distribution as red giants in general. This could either mean that the detected fields do not have a predominant impact on the redistribution of angular momentum, or that other red giants also harbour an internal field that is currently non-detectable or has not yet been detected.

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arXiv2024

Asteroseismic Signatures of Core Magnetism and Rotation in Hundreds of Low-Luminosity Red Giants

Red Giant stars host solar-like oscillations which have mixed character, being sensitive to conditions both in the outer convection zone and deep within the interior. The properties of these modes are sensitive to both core rotation and magnetic fields. While asteroseismic studies of the former have been done on a large scale, studies of the latter are currently limited to tens of stars. We aim to produce the first large catalogue of both magnetic and rotational perturbations. We jointly constrain these parameters by devising an automated method for fitting the power spectra directly. We successfully apply the method to 302 low-luminosity red giants. We find a clear bimodality in core rotation rate. The primary peak is at $δν_{\mathrm{rot}}$ = 0.32 $μ$Hz, and the secondary at $δν_{\mathrm{rot}}$ = 0.47 $μ$Hz. Combining our results with literature values, we find that the percentage of stars rotating much more rapidly than the population average increases with evolutionary state. We measure magnetic splittings of 2$σ$ significance in 23 stars. While the most extreme magnetic splitting values appear in stars with masses > 1.1M$_{\odot}$, implying they formerly hosted a convective core, a small but statistically significant magnetic splitting is measured at lower masses. Asymmetry between the frequencies of a rotationally split multiplet has previously been used to diagnose the presence of a magnetic perturbation. We find that of the stars with a significant detection of magnetic perturbation, 43\% do not show strong asymmetry. We find no strong evidence of correlation between the rotation and magnetic parameters.

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arXiv2024

Properties of observable mixed inertial and gravito-inertial modes in γ Doradus stars

In γ Doradus stars, gravito-inertial modes in the radiative zone and inertial modes in the convective core can interact resonantly, which translates into the appearance of dip structures in the period spacing of modes. Those dips are information-rich, as they are related to the star core characteristics. Our aim is to characterise these dips according to stellar properties and thus to develop new seismic diagnostic tools to constrain the internal structure of γ Doradus stars, especially their cores. We used the two-dimensional oscillation code TOP to compute sectoral prograde and axisymmetric dipolar modes in γ Doradus stars at different rotation rates and evolutionary stages. We then characterised the dips we obtained by their width and location on the period spacing diagram. We found that the width and the location of the dips depend quasi-linearly on the ratio of the rotation rate and the Brunt-Väisälä frequency at the core interface. This allowed us to determine empirical relations between the width and location of dips as well as the resonant inertial mode frequency in the core and the Brunt-Väisälä frequency at the interface between the convective core and the radiative zone. We propose an approximate theoretical model to support and discuss these empirical relations. The empirical relations we established could be applied to dips observed in data, which would allow for the estimation of frequencies of resonant inertial modes in the core and of the Brunt-Väisälä jump at the interface between the core and the radiative zone. As those two parameters are both related to the evolutionary stage of the star, their determination could lead to more accurate estimations of stellar ages.

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arXiv2023

Perturbative analysis of the effect of a magnetic field on gravito-inertial modes

Magnetic fields have been measured recently in the core of red giant stars thanks to their effects on stellar oscillation frequencies. The search for magnetic signatures in pulsating stars, such as $γ$ Doradus or Slowly Pulsation B stars, requires to adapt the formalism developed for the slowly rotating red giants to rapidly rotating stars. We perform a theoretical analysis of the effects of an arbitrary magnetic field on high radial order gravity and Rossby modes in a rapidly rotating star. The magnetic effects are treated as a perturbation. For high radial order modes, the contribution of the radial component of the magnetic field is likely to dominate over the azimuthal and latitudinal components. The rotation is taken into account through the traditional approximation of rotation. General expressions of the frequency shift induced by an arbitrary radial magnetic field are derived. Approximate analytical forms are obtained in the high-order high-spin-parameter limits for the modes most frequently observed in $γ$ Dor stars. We propose simple methods to detect seismic magnetic signatures and measure possible magnetic fields in such stars. These methods offer new possibilities to look for internal magnetic fields in future observations, such as the ones of the PLATO mission, or to revisit existing Kepler or TESS data.

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arXiv2023

Internal magnetic fields in 13 red giants detected by asteroseismology

While surface fields have been measured for stars across the HR diagram, internal magnetic fields remain largely unknown. The recent seismic detection of magnetic fields in the cores of several Kepler red giants has opened a new avenue to understand better the origin of magnetic fields and their impact on stellar structure and evolution. We aim to use asteroseismology to systematically search for internal magnetic fields in red giant stars and to determine the strengths and geometries of these fields. Magnetic fields are known to break the symmetry of rotational multiplets. In red giants, oscillation modes are mixed, behaving as pressure modes in the envelope and as gravity modes in the core. Magnetism-induced asymmetries are expected to be stronger for g-dominated modes than for p-dominated modes and to decrease with frequency. After collecting a sample of 2500 Kepler red giant stars with clear mixed-mode patterns, we specifically searched for targets among 1200 stars with dipole triplets. We identified 13 stars exhibiting clear asymmetric multiplets and measured their parameters, especially the asymmetry parameter and the magnetic frequency shift. By combining these estimates with best-fitting stellar models, we measured average core magnetic fields ranging from 20 to 150kG, corresponding to 5% to 30% of the critical field strengths. We showed that the detected core fields have various horizontal geometries, some of which significantly differ from a dipolar configuration. We found that the field strengths decrease with stellar evolution, despite the fact that the cores of these stars are contracting. Even though these stars have strong internal magnetic fields, they display normal core rotation rates, suggesting no significantly different histories of angular momentum transport compared to other red giant stars. We also discuss the possible origin of the detected fields.

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arXiv2022

30 to 100-kG magnetic fields in the cores of red giant stars

A red giant star is an evolved low- or intermediate-mass star that has exhausted its central hydrogen content, leaving a helium core and a hydrogen-burning shell. Oscillations of stars can be observed as periodic dimmings and brightenings in the optical light curves. In red giant stars, non-radial acoustic waves couple to gravity waves and give rise to mixed modes, which behave as pressure (p) modes in the envelope and gravity (g) modes in the core. These modes were previously used to measure the internal rotation of red giants, leading to the conclusion that purely hydrodynamical processes of angular momentum transport from the core are too inefficient. Magnetic fields could produce the additional required transport. However, due to the lack of direct measurements of magnetic fields in stellar interiors, very little is currently known about their properties. Asteroseismology can provide direct detection of magnetic fields because, like rotation, the fields induce shifts in the oscillation mode frequencies. Here we report the measurement of magnetic fields in the cores of three red giant stars observed with the Kepler satellite. The fields induce shifts that break the symmetry of dipole mode multiplets. We thus measure field strengths ranging from ~30 to ~100 kG in the vicinity of the hydrogen-burning shell and place constraints on the field tolopolgy.

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arXiv2019

Chronos --- Taking the pulse of our Galactic neighbourhood (ESA Voyage 2050 White Paper)

The period 2035-50 considered in the ESA Voyage long-term plan will coincide with a series of foreseeable advances in the characterization of the stellar content of the Milky Way. The Gaia mission, combined with large-scale spectroscopic surveys, is helping to build an unprecedented census in terms of the astrometric, kinematic and chemical properties of Galactic stellar populations. Within a decade, precise measurements of such properties will be available for hundreds of millions of stars. Meanwhile, time-domain surveys initiated with CoRoT and Kepler/K2 and carried on by space missions such as TESS and PLATO or ground-based projects like the LSST, will have brought asteroseismology to a high level of maturity. The combination of precise ages from asteroseismology with astrometric and spectroscopic data, on large stellar samples, is allowing Galactic archaeologists to gain new insight into the assembly history of the Milky Way. Recent breakthroughs --- based on the detection of solar-like oscillations in tens of thousands of red-giant stars --- demonstrate the potential of such approach. Therefore, we are convinced that an all-sky, high-cadence, long-duration stellar variability survey will become a scientific priority in the 2035-50 period. The Chronos concept presented here consists in a time-domain extension to Gaia. It will allow for mass and age estimates for half a million red giants within 1.7 kpc from the Sun and hence shed a new light on our understanding of the Galactic dynamics and archaeology. In terms of the targeted pulsators, Chronos will bridge the gap between PLATO and the LSST by surveying stars all the way from the subgiant branch to the early AGB. Finally, it will surpass all previous surveys capable of conducting asteroseismology in terms of the combined sky coverage and duration of the observations (2 x 3.75 months over the whole sky and >5 years in the CVZ).

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arXiv2018

Impact of general differential rotation on gravity waves in rapidly rotating stars

Differential rotation plays a key role in stellar evolution by triggering hydrodynamical instabilities and large-scale motions that induce transport of chemicals and angular momentum and by modifying the propagation and the frequency spectrum of gravito-inertial waves. It is thus crucial to investigate its effect on the propagation of gravity waves to build reliable seismic diagnostic tools, especially for fast rotating stars, where perturbative treatments of rotation fail. Generalising a previous work done in the case of uniform rotation, we derived a local dispersion relation for gravity waves in a differentially rotating star, taking the full effect of rotation (both Coriolis and centrifugal accelerations) into account. Then we modelled the propagation of axisymmetric waves as the propagation of rays. This allowed us to efficiently probe the properties of the waves in various regimes of differential rotation.

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arXiv2018

Asymptotic theory of gravity modes in rotating stars II. Impact of general differential rotation

Context. Differential rotation has a strong influence on stellar internal dynamics and evolution, notably by triggering hydrodynamical instabilities, by interacting with the magnetic field, and more generally by inducing transport of angular momentum and chemical elements. Moreover, it modifies the way waves propagate in stellar interiors and thus the frequency spectrum of these waves, the regions they probe, and the transport they generate. Aims. We investigate the impact of a general differential rotation (both in radius and latitude) on the propagation of axisymmetric gravito-inertial waves. Methods. We use a small-wavelength approximation to obtain a local dispersion relation for these waves. We then describe the propagation of waves thanks to a ray model that follows a Hamiltonian formalism. Finally, we numerically probe the properties of these gravito-inertial rays for different regimes of radial and latitudinal differential rotation. Results. We derive a local dispersion relation that includes the effect of a general differential rotation. Subsequently, considering a polytropic stellar model, we observe that differential rotation allows for a large variety of resonant cavities that can be probed by gravito-inertial waves. We identify that for some regimes of frequency and differential rotation, the properties of gravito-inertial rays are similar to those found in the uniformly rotating case. Furthermore, we also find new regimes specific to differential rotation, where the dynamics of rays is chaotic. Conclusions. As a consequence, we expect modes to follow the same trend. Some parts of oscillation spectra corresponding to regimes similar to those of the uniformly rotating case would exhibit regular patterns, while parts corresponding to the new regimes would be mostly constituted of chaotic modes with a spectrum rather characterised by a generic statistical distribution.

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arXiv2017

Non-adiabatic oscillations of fast-rotating stars: the example of Rasalhague

Early-type stars generally tend to be fast rotators. In these stars, mode identification is very challenging as the effects of rotation are not well known. We consider here the example of $α$ Ophiuchi, for which dozens of oscillation frequencies have been measured. We model the star using the two-dimensional structure code ESTER, and we compute both adiabatic and non-adiabatic oscillations using the TOP code. Both calculations yield very complex spectra, and we used various diagnostic tools to try and identify the observed pulsations. While we have not reached a satisfactory mode-to-mode identification, this paper presents promising early results.

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arXiv2016

Period spacing of gravity modes strongly affected by rotation. Going beyond the traditional approximation

Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration, which can be used to probe stellar internal structure and rotation. Methods. We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the EBK quantisation method to compute modes frequencies from rays. Results. Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions. The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as $γ$ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.

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arXiv2016

Seismic diagnosis from gravity modes strongly affected by rotation

Most of the information we have about the internal rotation of stars comes from modes that are weakly affected by rotation, for example by using rotational splittings. In contrast, we present here a method, based on the asymptotic theory of Prat et al. (2016), which allows us to analyse the signature of rotation where its effect is the most important, that is in low-frequency gravity modes that are strongly affected by rotation. For such modes, we predict two spectral patterns that could be confronted to observed spectra and those computed using fully two-dimensional oscillation codes.

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arXiv2016

Gravito-inertial waves in a differentially rotating spherical shell

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.

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arXiv2016

Asymptotic theory of gravity modes in rotating stars. I. Ray dynamics

Context. The seismology of early-type stars is limited by our incomplete understanding of gravito-inertial modes. Aims. We develop a short-wavelength asymptotic analysis for gravito-inertial modes in rotating stars. Methods. The Wentzel-Kramers-Brillouin approximation was applied to the equations governing adiabatic small perturbations about a model of a uniformly rotating barotropic star. Results. A general eikonal equation, including the effect of the centrifugal deformation, is derived. The dynamics of axisymmetric gravito-inertial rays is solved numerically for polytropic stellar models of increasing rotation and analysed by describing the structure of the phase space. Three different types of phase-space structures are distinguished. The first type results from the continuous evolution of structures of the non-rotating integrable phase space. It is predominant in the low-frequency part of the phase space. The second type of structures are island chains associated with stable periodic rays. The third type of structures are large chaotic regions that can be related to the envelope minimum of the Brunt-Väisälä frequency. Conclusions. Gravito-inertial modes are expected to follow this classification, in which the frequency spectrum is a superposition of sub-spectra associated with these different types of phase-space structures. The detailed confrontation between the predictions of this ray-based asymptotic theory and numerically computed modes will be presented in a companion paper.

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arXiv2014

Gravito-inertial modes in a differentially rotating spherical shell

While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes.

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arXiv2014

Gap interpolation by inpainting methods : Application to Ground and Space-based Asteroseismic data

In asteroseismology, the observed time series often suffers from incomplete time coverage due to gaps. The presence of periodic gaps may generate spurious peaks in the power spectrum that limit the analysis of the data. Various methods have been developed to deal with gaps in time series data. However, it is still important to improve these methods to be able to extract all the possible information contained in the data. In this paper, we propose a new approach to handle the problem, the so-called inpainting method. This technique, based on a sparsity prior, enables to judiciously fill-in the gaps in the data, preserving the asteroseismic signal, as far as possible. The impact of the observational window function is reduced and the interpretation of the power spectrum is simplified. This method is applied both on ground and space-based data. It appears that the inpainting technique improves the oscillation modes detection and estimation. Additionally, it can be used to study very long time series of many stars because its computation is very fast. For a time series of 50 days of CoRoT-like data, it allows a speed-up factor of 1000, if compared to methods of the same accuracy.

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arXiv2014

Gravito-inertial modes in a differentially rotating spherical shell

Oscillations have been detected in a variety of stars, including intermediate- and high-mass main sequence stars. While many of these stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study on axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. These modes probe the deep layers of the star around its convective core. We consider a simplified model where the radiative zone of a star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral simulations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We characterise these attractors by the dependence of their Lyapunov exponent with the \BV frequency of the background and the oscillation frequency of the mode. Finally, we note that, as modes associated with short-period attractors form dissipative structures, they could play an important role for tidal interactions but should be dismissed in the interpretation of observed oscillation frequencies.

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